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Chapter 4: Q1E (page 981)

A single loop of wire with an area of 0.0900m2is in a uniform magnetic field that has an initial value of 3.80 T, is perpendicular to the plane of the loop, and is decreasing at a constant rate of 0.190 T/s. (a) What emf is induced in this loop? (b) If the loop has a resistance of 0.600 鈩�, find the current induced in the loop.

Short Answer

Expert verified
  1. Emf induced in the loop is 蔚=0.0171V
  2. Current induced in the loop is l = 0.0285A

Step by step solution

01

Magnetic flux

a. Consider a single loop of wire with an Area A=0.0900m2 that is placed perpendicularly in a magnetic field with an initial value of B = 3.80 T and a constant rate of dBdT=0.190Ts decrease. Consequently, the magnitude of the induced emf is given by

蔚=d桅Bdt

Here,

桅B=BAcos蠒

Putting 蠒=0掳, so the equation is;

蔚=AdBdt

On putting the values;

蔚=0.0900m20.190T/s蔚=0.0171V

Hence, the Emf induced in the loop is蔚=0.0171V

02

Induced current

b. If the resistance of the loop is R=0.600惟, the induced current is

l=蔚R=0.0171V0.600惟l=0.0285A

Hence, the current induced in the loop isl=0.0285A

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